Abstract
Let be an algebraically closed field of characteristic zero and the additive group of . An algebraic variety is said to be flexible if the tangent space at every regular point of is generated by the tangent vectors to orbits of various regular actions of . In 1972, Vinberg and Popov introduced the class of affine -varieties which are also known as affine horospherical varieties. These are varieties on which a connected algebraic group acts with an open orbit in such a way that the stationary subgroup of each point in the orbit contains a maximal unipotent subgroup of . In this paper the flexibility of affine horospherical varieties of semisimple groups is proved. Bibliography: 9 titles.
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